# Almost-K\"ahler anti-self-dual metrics on $K3\#3\overline{\mathbb{CP}_{2}}$

## TL;DR

This paper demonstrates the existence of almost-Kähler metrics within certain anti-self-dual conformal classes on the complex surface $K3 ext{ extperiodcentered}3ar{ ext{ exttwosuperior}} ext{ extbackslash}CP^{2}$, expanding understanding of geometric structures on this manifold.

## Contribution

It shows that some anti-self-dual classes constructed by Donaldson-Friedman admit almost-Kähler representatives, a new insight into the geometry of these classes.

## Key findings

- Existence of almost-Kähler metrics in specific anti-self-dual classes
- Application of twistor space methods to identify geometric structures
- Extension of known anti-self-dual constructions to include almost-Kähler structures

## Abstract

Donaldson-Friedman constructed anti-self-dual classes on $K3\#3\overline{\mathbb{CP}_{2}}$ using twistor space. We show that some of these conformal classes have almost-K\"ahler representatives.